David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Nonlinear Analysis Series A 72 (3-4):1701-1708 (2010)
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different accuracies. The traditional and the new approaches are compared and discussed.
|Keywords||The First Hilbert problem|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
G. Kreisel (1953). A Variant to Hilbert's Theory of the Foundations of Arithmetic. British Journal for the Philosophy of Science 4 (14):107-129.
Alexey Kryukov (2004). On the Problem of Emergence of Classical Space—Time: The Quantum-Mechanical Approach. Foundations of Physics 34 (8):1225-1248.
Kai F. Wehmeier (1997). Aspekte der frege–hilbert-korrespondenz. History and Philosophy of Logic 18 (4):201-209.
Jairo José Da Silva (2000). Husserl's Two Notions of Completeness: Husserl and Hilbert on Completeness and Imaginary Elements in Mathematics. Synthese 125 (3):417 - 438.
Philip Kitcher (1976). Hilbert's Epistemology. Philosophy of Science 43 (1):99-115.
Yaroslav Sergeyev & Alfredo Garro (2010). Observability of Turing Machines: A Refinement of the Theory of Computation. Informatica 21 (3):425–454.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
José Ferreirós (2009). Hilbert, Logicism, and Mathematical Existence. Synthese 170 (1):33 - 70.
Yaroslav Sergeyev (2007). Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers. Chaos, Solitons and Fractals 33 (1):50-75.
C. S. Calude & G. J. Chaitin (1999). Randomness Everywhere. Nature 400:319-320.
Added to index2009-12-03
Total downloads10 ( #235,023 of 1,726,249 )
Recent downloads (6 months)4 ( #183,604 of 1,726,249 )
How can I increase my downloads?